= Solution
For the <Double-degenerate Type Ia supernova scenario>, measure the <Type Ia supernova> rate per formed stellar mass in old galaxies, grouped by the time since their main star-formation episode. Correct the event counts for observing time and detection efficiency. In an ideal burst population, the normalized rate measures the <delay-time distribution> directly. If <gravitational waves> inspiral dominates the delay and the initial white-dwarf separations are uniformly distributed in separation, <3/c> predicts a slope $-3/4$.
More generally, if $dN/dA\propto A^\beta$ and $t_m\propto A^4$, the predicted rate scales as $t_m^{(\beta-3)/4}$. A distribution uniform in $\log A$ has $\beta=-1$ and gives $t_m^{-1}$. Thus a slope differing from $-3/4$ does not alone rule out mergers: the separation distribution must also be tested.
An extended <star formation history> gives a convolution, $R(t)=\int d\tau\,\mathrm{SFR}(t-\tau)\Psi(\tau)$, rather than the single-burst expression. The time since <star formation> stopped need not equal each progenitor's age. Stellar lifetimes before formation of the second <white dwarf>, common-envelope evolution, masses and mass ratios, metallicity, delay-dependent explosion efficiencies, galaxy-age estimates and survey selection all affect the comparison. Some CO-white-dwarf mergers need not make <Type Ia supernovae>, and other channels can contribute to the observed rate. Agreement in slope and normalization therefore supports the hypothesis under stated assumptions but is not a unique identification of the channel.
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